FOLDING OF 2-MANIFOLDS

Abstract

The project of this thesis concerns a field of mathematics called "Geometric Topology", which essentially studies various structures and properties of manifolds and complexes.

Ismoetric foldings between Riemannian manifolds may be characterized as maps that send piecewise geodesic segments to piecewise geodesic segments of the same length.

The field of isometric foldings began with Robertson's, work [20] who studied the stratification determined by the folds or the singularities, and relates this structure to classical ideas of Hopff degree, and volume. Then the theory of isometric foldings, has been pushed by both Robertson and El-Kholy [21] to include covering spaces and many other different aspects. Again the idea of topological folding is modeled by both of themonthat of isometric folding, but in the absence of metrical structure [7].